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Quiz 6 Examples 2013
Example 1.
RNAqua, Inc., has patented backward water, OH
2
. The demand curve is a
straight line with a vertical intercept of $190 per gram and a horizontal intercept of 950
grams. The marginal cost of each extra unit is $10. What is RNAqua’s maximum
revenue?
RNAqua will set the price at
0.5 x ($190 + $10) = $100, the midpoint between the
marginal cost and the vertical intercept of the demand curve.
The demand curve is
Q = 950 – (950/190)P = 950 – 5P.
At P = 100, Q = 450 and profit is (10010) x 450 =
$40,500.
By the way, to illustrate (though not prove) why RNAqua sets the price at $100,
suppose they set it at $99.
Then profit would be $89 x 455 = $40,495.
Suppose they set
it at $101. Then profit would be $91 x 445 = $40,495.
Two things to notice:
(1) The
maximum profit is at P = $100, by the Battle for Midway rule, and (2) if they miss the
optimal price by 1%, that reduces their profit by only one hundredth of 1%, or one part in
10,000.
If marginal cost or demand varies slightly, RNAqua may not want to risk
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 Fall '05
 Denslow
 Macroeconomics

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